Games With the Best Odds in Vegas 1. Blackjack – House edge 1% – 2%. Image: ‘Blackjack board’ is licensed under Wikimedia Commons. Blackjack is a game of chance – for you and for the. Blackjack should need no introduction. It is the most popular table game in the United States, and is easily found in casinos throughout the world. The object of the game of Blackjack is simply to get more points than the dealer without going over 21. Rules Hand Signals Wizard’s Simple Strategy Basic Strategy Blackjack. You have a 1/20 prob. Of being dealt a blackjack w only a 1/25 chance (assuming 8-deck shoe) of having your blackjack pushed. Suppose you are playing a 13 loss Martingale, then that means you will have 200 strings that end with you getting a blackjack and making $10 plus your bet on the string. The Blackjack Odds and the House Advantage. To fully get into the game of blackjack, you have to understand and if possible, master the blackjack odds and house advantages. It is very crucial to know how the casino gets their edge and how it helps them win. It's important to be aware of the blackjack odds like the odds of being dealt a.
Blackjack is unlike many other casino games because the player is actively involved in the outcome of his hands (rather than betting on a random event over which he has no influcene). As a result, a player’s chances of winning depend on not only the random outcome of the draw but also upon the decisions he makes during the game—to hit or to stand, to exercise options such as doubling or splitting.
Chances of Winning Blackjack
Throughout several rounds, the chances of winning each hand will also be skewed by the cards that have been removed from the deck. The player’s net loss or gain (the amount in money, rather than a tally of hands won or lost) over a session will be affected by how much he wagers, and at which times he elects to increase or decrease the wagered amount. Finally, house rules can be imposed to change the parameters of the game and restrict the player’s options.
With all of these factors in effect, it’s not possible to affix a specific number to all situations or all styles of play—but three figures are often cited:
- Most casinos expect each blackjack table to have a hold of about 20%—that is, they expect to be able to keep about 20% of the wagers made. Correspondingly, the average player can expect to lose about 20% of his stake over the course of every session.
- The “core odds” reduce the house’s advantage to 10.99%. Based on the assumption the player will elect to hit or stand by the same criteria as the house, the house will win roughly 10.99% more hands than the player.
- The net odds—which consider the amount of money won or lost rather than the core number of hands, generally work out to an 8.89% advantage to the house (given a two-deck game played by the most common set of rules).
An interesting, if somewhat premature, note on these figures is that the house expects to earn more than double (20% as compared to 8.89%) what the odds would seem to indicate it will and that these expectations generally hold. This demonstrates how the player’s decisions can affect the outcome of the game—and that the average player will lose more than double the mathematically probably amount because of uninformed decisions.
The basic blackjack, intermediate, and advanced blackjack strategies described in the blackjack strategy section of this site can further impact the odds. By using blackjack basic strategy consistently, the player can decrease the house’s advantage to less than 1%. By adding the intermediate and advanced strategies, a player can make the game completely even (hence fair) and, in rare situations, also turn the odds in his favour by a fraction of a percentage.
What are Odds?
In its purest sense, odds are the chances a given outcome will occur given the possible alternatives. The most comfortable metaphor is a coin toss: if a coin is tossed in a genuinely random fashion (nothing influences the outcome), it is just as likely to come up heads as tails. If it is tossed ten times, you can expect it to come up heads five times, and tails five times.
Granted, it is possible, even with true randomness, that the toss will result in heads ten times in a row—which is why odds consider likely rather than specific outcomes. In the long run, the mathematical probability will bear itself out in practice—if a coin is tossed 1,000 times, it is likely to come up heads 500 times (though, in practice, it will be plus or minus a few). Thus, it’s not necessary to spend several years flipping a coin million of times to determine the likely outcomes or rig a supercomputer to simulate the same—though some stubbornly have.
Casino games are carefully designed to exploit the odds, always taking advantage for the house: a player will never be paid a wager that is strictly equal to the true odds. A good example of this practice is roulette, in which a wager on a single number pays 35 to 1 even though the odds of winning are 1 in 37.
What are the odds of winning blackjack
Blackjack, however, foils the computation of odds based on random events because there are a number of influences that prevent it from being completely random—most significantly the player’s choices during the course of the game. In such cases, the odds are set to turn a reasonable profit from the average player. (Actually, they’re set to turn a reasonable profit from the reasonable intelligent player, an exorbitant one from the average player, and flat-out milk a “sucker.”) This is why an attentive player who makes the right decisions can come out ahead.
The odds of the hand’s outcome are determined not only by the initial hand dealt and by the number of hits that are added. This can vary greatly, because a player can take as many or as few as he desires—a player may opt to hit every hand he is dealt until it exceeds 21 and lose 100% of the time.
We can, however, be reasonably certain of the dealer’s behavior, as he is forced to play by certain rules, regardless of his instincts, superstitions, or desires. Most often, the rules require the dealer to stop taking hits when his hand reaches a total of seventeen or greater, and no sooner. Before the cards are dealt, it’s possible to predict the chances that the dealer’s hand will have the following outcomes.
Blackjack win percentage
All the totals for hands remain equal—so a player’s 20 will beat a dealer’s 19 equally as often as a dealer’s 20 beats a player’s 19, and the dealer will bust as often as the player while the other stands on a viable hand. The only remaining difference is that the dealer will bust of the instances in which the player busts—which is 33.15% likely to happen in 33.15% of the time, for a core odds value of 10.99% of all hands played.
17 | 18 | 19 | 20 | 21 | BUST |
---|---|---|---|---|---|
14.61% | 13.87% | 13.27% | 18.12% | 6.99% | 33.15% |
These odds are computed according to mathematical probabilities. More detailed information is available on the blackjack hand calculator post.
The outcome of the player’s hand, meanwhile, will depend on the way his hands are played. If he chooses exactly the same course as the dealer, the outcome of his hands will be exactly the same as is shown above. If he plays according to a different set of rules, the results will be different, and by comparing the two tables, that player’s individual likelihood of winning can be computed. If however, the player is erratic, and he chooses to play his hands differently each time with no predictable rationale, no mathematical model can be used to compute his chances of winning.
Determining the core odds
The “core odds” of the game assume that the player will follow the house rules for hitting his hands. In this example, to stop taking hits when his hand reaches a total of seventeen or greater, and no sooner. In this case, all things seem to be equal, and the player should have a 50% chance of winning or losing each hand. This would be true only if the player’s wager was returned the dealer busts his hand but one rule of the game that is never varied is that a player who busts loses his wager, even if the dealer busts afterward.
Again, the core odds shown here apply only to a player who strictly adheres to the same rules as the dealer in playing his hands, which is clearly not the best approach. The strategy section of this site will demonstrate a system that can virtually eliminate the house’s advantage over the player—and the intermediate and advanced sections will turn the tables further in the player’s advantage.
One of the most interesting aspects of blackjack is the
probability math involved. It’s more complicated than other
games. In fact, it’s easier for computer programs to calculate
blackjack probability by running billions of simulated hands
than it is to calculate the massive number of possible outcomes.
probability math involved. It’s more complicated than other
games. In fact, it’s easier for computer programs to calculate
blackjack probability by running billions of simulated hands
than it is to calculate the massive number of possible outcomes.
This page takes a look at how blackjack probability works. It
also includes sections on the odds in various blackjack
situations you might encounter.
also includes sections on the odds in various blackjack
situations you might encounter.
An Introduction to Probability
Probability is the branch of mathematics that deals with the
likelihood of events. When a meteorologist estimates a 50%
chance of rain on Tuesday, there’s more than meteorology at
work. There’s also math.
likelihood of events. When a meteorologist estimates a 50%
chance of rain on Tuesday, there’s more than meteorology at
work. There’s also math.
Probability is also the branch of math that governs gambling.
After all, what is gambling besides placing bets on various
events? When you can analyze the payoff of the bet in relation
to the odds of winning, you can determine whether or not a bet
is a long term winner or loser.
After all, what is gambling besides placing bets on various
events? When you can analyze the payoff of the bet in relation
to the odds of winning, you can determine whether or not a bet
is a long term winner or loser.
The Probability Formula
The basic formula for probability is simple. You divide the
number of ways something can happen by the total possible number
of events.
number of ways something can happen by the total possible number
of events.
Here are three examples.
Example 1:You want to determine the probability of getting heads when
you flip a coin. You only have one way of getting heads, but
there are two possible outcomes—heads or tails. So the
probability of getting heads is 1/2.
Example 2:you flip a coin. You only have one way of getting heads, but
there are two possible outcomes—heads or tails. So the
probability of getting heads is 1/2.
You want to determine the probability of rolling a 6 on a
standard die. You have one possible way of rolling a six, but
there are six possible results. Your probability of rolling a
six is 1/6.
Example 3:standard die. You have one possible way of rolling a six, but
there are six possible results. Your probability of rolling a
six is 1/6.
You want to determine the probability of drawing the ace of
spades out of a deck of cards. There’s only one ace of spades in
a deck of cards, but there are 52 cards total. Your probability
of drawing the ace of spades is 1/52.
spades out of a deck of cards. There’s only one ace of spades in
a deck of cards, but there are 52 cards total. Your probability
of drawing the ace of spades is 1/52.
A probability is always a number between 0 and 1. An event
with a probability of 0 will never happen. An event with a
probability of 1 will always happen.
with a probability of 0 will never happen. An event with a
probability of 1 will always happen.
Here are three more examples.
Example 4:You want to know the probability of rolling a seven on a
single die. There is no seven, so there are zero ways for this
to happen out of six possible results. 0/6 = 0.
single die. There is no seven, so there are zero ways for this
to happen out of six possible results. 0/6 = 0.
Example 5:
You want to know the probability of drawing a joker out of a
deck of cards with no joker in it. There are zero jokers and 52
possible cards to draw. 0/52 = 0.
Example 6:deck of cards with no joker in it. There are zero jokers and 52
possible cards to draw. 0/52 = 0.
You have a two headed coin. Your probability of getting heads
is 100%. You have two possible outcomes, and both of them are
heads, which is 2/2 = 1.
is 100%. You have two possible outcomes, and both of them are
heads, which is 2/2 = 1.
A fraction is just one way of expressing a probability,
though. You can also express fractions as a decimal or a
percentage. So 1/2 is the same as 0.5 and 50%.
though. You can also express fractions as a decimal or a
percentage. So 1/2 is the same as 0.5 and 50%.
You probably remember how to convert a fraction into a
decimal or a percentage from junior high school math, though.
decimal or a percentage from junior high school math, though.
Expressing a Probability in Odds Format
The more interesting and useful way to express probability is
in odds format. When you’re expressing a probability as odds,
you compare the number of ways it can’t happen with the number
of ways it can happen.
in odds format. When you’re expressing a probability as odds,
you compare the number of ways it can’t happen with the number
of ways it can happen.
Here are a couple of examples of this.
Example 1:You want to express your chances of rolling a six on a six
sided die in odds format. There are five ways to get something
other than a six, and only one way to get a six, so the odds are
5 to 1.
Example 2:sided die in odds format. There are five ways to get something
other than a six, and only one way to get a six, so the odds are
5 to 1.
You want to express the odds of drawing an ace of spades out
a deck of cards. 51 of those cards are something else, but one
of those cards is the ace, so the odds are 51 to 1.
a deck of cards. 51 of those cards are something else, but one
of those cards is the ace, so the odds are 51 to 1.
Odds become useful when you compare them with payouts on
bets. True odds are when a bet pays off at the same rate as its
probability.
bets. True odds are when a bet pays off at the same rate as its
probability.
Here’s an example of true odds:
You and your buddy are playing a simple gambling game you
made up. He bets a dollar on every roll of a single die, and he
gets to guess a number. If he’s right, you pay him $5. If he’s
wrong, he pays you $1.
made up. He bets a dollar on every roll of a single die, and he
gets to guess a number. If he’s right, you pay him $5. If he’s
wrong, he pays you $1.
Since the odds of him winning are 5 to 1, and the payoff is
also 5 to 1, you’re playing a game with true odds. In the long
run, you’ll both break even. In the short run, of course,
anything can happen.
also 5 to 1, you’re playing a game with true odds. In the long
run, you’ll both break even. In the short run, of course,
anything can happen.
Probability and Expected Value
One of the truisms about probability is that the greater the
number of trials, the closer you’ll get to the expected results.
number of trials, the closer you’ll get to the expected results.
If you changed the equation slightly, you could play this
game at a profit. Suppose you only paid him $4 every time he
won. You’d have him at an advantage, wouldn’t you?
game at a profit. Suppose you only paid him $4 every time he
won. You’d have him at an advantage, wouldn’t you?
- He’d win an average of $4 once every six rolls
- But he’d lose an average of $5 on every six rolls
- This gives him a net loss of $1 for every six rolls.
You can reduce that to how much he expects to lose on every
single roll by dividing $1 by 6. You’ll get 16.67 cents.
single roll by dividing $1 by 6. You’ll get 16.67 cents.
On the other hand, if you paid him $7 every time he won, he’d
have an advantage over you. He’d still lose more often than he’d
win. But his winnings would be large enough to compensate for
those 5 losses and then some.
have an advantage over you. He’d still lose more often than he’d
win. But his winnings would be large enough to compensate for
those 5 losses and then some.
The difference between the payout odds on a bet and the true
odds is where every casino in the world makes its money. The
only bet in the casino which offers a true odds payout is the
odds bet in craps, and you have to make a bet at a disadvantage
before you can place that bet.
odds is where every casino in the world makes its money. The
only bet in the casino which offers a true odds payout is the
odds bet in craps, and you have to make a bet at a disadvantage
before you can place that bet.
Here’s an actual example of how odds work in a casino. A
roulette wheel has 38 numbers on it. Your odds of picking the
correct number are therefore 37 to 1. A bet on a single number
in roulette only pays off at 35 to 1.
roulette wheel has 38 numbers on it. Your odds of picking the
correct number are therefore 37 to 1. A bet on a single number
in roulette only pays off at 35 to 1.
You can also look at the odds of multiple events occurring.
The operative words in these situations are “and” and “or”.
The operative words in these situations are “and” and “or”.
- If you want to know the probability of A happening AND
of B happening, you multiply the probabilities. - If you want to know the probability of A happening OR of
B happening, you add the probabilities together.
Here are some examples of how that works.
Example 1:You want to know the probability that you’ll draw an ace of
spades AND then draw the jack of spades. The probability of
drawing the ace of spades is 1/52. The probability of then
drawing the jack of spades is 1/51. (That’s not a typo—you
already drew the ace of spades, so you only have 51 cards left
in the deck.)
spades AND then draw the jack of spades. The probability of
drawing the ace of spades is 1/52. The probability of then
drawing the jack of spades is 1/51. (That’s not a typo—you
already drew the ace of spades, so you only have 51 cards left
in the deck.)
The probability of drawing those 2 cards in that order is
1/52 X 1/51, or 1/2652.
Example 2:1/52 X 1/51, or 1/2652.
You want to know the probability that you’ll get a blackjack.
That’s easily calculated, but it varies based on how many decks
are being used. For this example, we’ll use one deck.
That’s easily calculated, but it varies based on how many decks
are being used. For this example, we’ll use one deck.
To get a blackjack, you need either an ace-ten combination,
or a ten-ace combination. Order doesn’t matter, because either
will have the same chance of happening.
or a ten-ace combination. Order doesn’t matter, because either
will have the same chance of happening.
Your probability of getting an ace on your first card is
4/52. You have four aces in the deck, and you have 52 total
cards. That reduces down to 1/13.
4/52. You have four aces in the deck, and you have 52 total
cards. That reduces down to 1/13.
Your probability of getting a ten on your second card is
16/51. There are 16 cards in the deck with a value of ten; four
each of a jack, queen, king, and ten.
16/51. There are 16 cards in the deck with a value of ten; four
each of a jack, queen, king, and ten.
So your probability of being dealt an ace and then a 10 is
1/13 X 16/51, or 16/663.
1/13 X 16/51, or 16/663.
The probability of being dealt a 10 and then an ace is also
16/663.
16/663.
You want to know if one or the other is going to happen, so
you add the two probabilities together.
you add the two probabilities together.
16/663 + 16/663 = 32/663.
That translates to approximately 0.0483, or 4.83%. That’s
about 5%, which is about 1 in 20.
Example 3:about 5%, which is about 1 in 20.
You’re playing in a single deck blackjack game, and you’ve
seen 4 hands against the dealer. In all 4 of those hands, no ace
or 10 has appeared. You’ve seen a total of 24 cards.
seen 4 hands against the dealer. In all 4 of those hands, no ace
or 10 has appeared. You’ve seen a total of 24 cards.
What is your probability of getting a blackjack now?
Your probability of getting an ace is now 4/28, or 1/7.
(There are only 28 cards left in the deck.)
(There are only 28 cards left in the deck.)
Your probability of getting a 10 is now 16/27.
Your probability of getting an ace and then a 10 is 1/7 X
16/27, or 16/189.
16/27, or 16/189.
Again, you could get a blackjack by getting an ace and a ten
or by getting a ten and then an ace, so you add the two
probabilities together.
or by getting a ten and then an ace, so you add the two
probabilities together.
16/189 + 16/189 = 32/189
Your chance of getting a blackjack is now 16.9%.
This last example demonstrates why counting cards works. The
deck has a memory of sorts. If you track the ratio of aces and
tens to the low cards in the deck, you can tell when you’re more
likely to be dealt a blackjack.
deck has a memory of sorts. If you track the ratio of aces and
tens to the low cards in the deck, you can tell when you’re more
likely to be dealt a blackjack.
Since that hand pays out at 3 to 2 instead of even money,
you’ll raise your bet in these situations.
you’ll raise your bet in these situations.
The House Edge
The house edge is a related concept. It’s a calculation of
your expected value in relation to the amount of your bet.
your expected value in relation to the amount of your bet.
Here’s an example.
If the expected value of a $100 bet is $95, the house edge is
5%.
5%.
Expected value is just the average amount of money you’ll win
or lose on a bet over a huge number of trials.
or lose on a bet over a huge number of trials.
Using a simple example from earlier, let’s suppose you are a
12 year old entrepreneur, and you open a small casino on the
street corner. You allow your customers to roll a six sided die
and guess which result they’ll get. They have to bet a dollar,
and they get a $4 win if they’re right with their guess.
12 year old entrepreneur, and you open a small casino on the
street corner. You allow your customers to roll a six sided die
and guess which result they’ll get. They have to bet a dollar,
and they get a $4 win if they’re right with their guess.
Over every six trials, the probability is that you’ll win
five bets and lose one bet. You win $5 and lose $4 for a net win
of $1 for every 6 bets.
five bets and lose one bet. You win $5 and lose $4 for a net win
of $1 for every 6 bets.
$1 divided by six bets is 16.67 cents.
Your house edge is 16.67% for this game.
Your house edge is 16.67% for this game.
The expected value of that $1 bet, for the customer, is about
84 cents. The expected value of each of those bets–for you–is
$1.16.
84 cents. The expected value of each of those bets–for you–is
$1.16.
That’s how the casino does the math on all its casino games,
and the casino makes sure that the house edge is always in their
favor.
and the casino makes sure that the house edge is always in their
favor.
With blackjack, calculating this house edge is harder. After
all, you have to keep up with the expected value for every
situation and then add those together. Luckily, this is easy
enough to do with a computer. We’d hate to have to work it out
with a pencil and paper, though.
all, you have to keep up with the expected value for every
situation and then add those together. Luckily, this is easy
enough to do with a computer. We’d hate to have to work it out
with a pencil and paper, though.
What does the house edge for blackjack amount to, then?
It depends on the game and the rules variations in place. It
also depends on the quality of your decisions. If you play
perfectly in every situation—making the move with the highest
possible expected value—then the house edge is usually between
0.5% and 1%.
also depends on the quality of your decisions. If you play
perfectly in every situation—making the move with the highest
possible expected value—then the house edge is usually between
0.5% and 1%.
If you just guess at what the correct play is in every
situation, you can add between 2% and 4% to that number. Even
for the gambler who ignores basic strategy, blackjack is one of
the best games in the casino.
situation, you can add between 2% and 4% to that number. Even
for the gambler who ignores basic strategy, blackjack is one of
the best games in the casino.
Expected Hourly Loss and/or Win
You can use this information to estimate how much money
you’re liable to lose or win per hour in the casino. Of course,
this expected hourly win or loss rate is an average over a long
period of time. Over any small number of sessions, your results
will vary wildly from the expectation.
you’re liable to lose or win per hour in the casino. Of course,
this expected hourly win or loss rate is an average over a long
period of time. Over any small number of sessions, your results
will vary wildly from the expectation.
What Are The Odds Of Craps
Here’s an example of how that calculation works.
- You are a perfect basic strategy player in a game with a
0.5% house edge. - You’re playing for $100 per hand, and you’re averaging
50 hands per hour. - You’re putting $5,000 into action each hour ($100 x 50).
- 0.5% of $5,000 is $25.
- You’re expected (mathematically) to lose $25 per hour.
Blackjack Odds Chart Printable
Here’s another example that assumes you’re a skilled card
counter.
counter.
- You’re able to count cards well enough to get a 1% edge
over the casino. - You’re playing the same 50 hands per hour at $100 per
hand. - Again, you’re putting $5,000 into action each hour ($100
x $50). - 1% of $5,000 is $50.
- Now, instead of losing $25/hour, you’re winning $50 per
hour.
Effects of Different Rules on the House Edge
The conditions under which you play blackjack affect the
house edge. For example, the more decks in play, the higher the
house edge. If the dealer hits a soft 17 instead of standing,
the house edge goes up. Getting paid 6 to 5 instead of 3 to 2
for a blackjack also increases the house edge.
house edge. For example, the more decks in play, the higher the
house edge. If the dealer hits a soft 17 instead of standing,
the house edge goes up. Getting paid 6 to 5 instead of 3 to 2
for a blackjack also increases the house edge.
What Are The Odds Of Poker Hands
Luckily, we know the effect each of these changes has on the
house edge. Using this information, we can make educated
decisions about which games to play and which games to avoid.
house edge. Using this information, we can make educated
decisions about which games to play and which games to avoid.
Here’s a table with some of the effects of various rule
conditions.
conditions.
Rules Variation | Effect on House Edge |
---|---|
6 to 5 payout on a natural instead of the stand 3 to 2 payout | +1.3% |
Not having the option to surrender | +0.08% |
8 decks instead of 1 deck | +0.61% |
Dealer hits a soft 17 instead of standing | +0.21% |
Player is not allowed to double after splitting | +0.14% |
Player is only allowed to double with a total of 10 or 11 | +0.18% |
Player isn’t allowed to re-split aces | +0.07% |
Player isn’t allow to hit split aces | +0.18% |
These are just some examples. There are multiple rules
variations you can find, some of which are so dramatic that the
game gets a different name entirely. Examples include Spanish 21
and Double Exposure.
variations you can find, some of which are so dramatic that the
game gets a different name entirely. Examples include Spanish 21
and Double Exposure.
The composition of the deck affects the house edge, too. We
touched on this earlier when discussing how card counting works.
But we can go into more detail here.
touched on this earlier when discussing how card counting works.
But we can go into more detail here.
Every card that is removed from the deck moves the house edge
up or down on the subsequent hands. This might not make sense
initially, but think about it. If you removed all the aces from
the deck, it would be impossible to get a 3 to 2 payout on a
blackjack. That would increase the house edge significantly,
wouldn’t it?
up or down on the subsequent hands. This might not make sense
initially, but think about it. If you removed all the aces from
the deck, it would be impossible to get a 3 to 2 payout on a
blackjack. That would increase the house edge significantly,
wouldn’t it?
Here’s the effect on the house edge when you remove a card of
a certain rank from the deck.
a certain rank from the deck.
Card Rank | Effect on House Edge When Removed |
---|---|
2 | -0.40% |
3 | -0.43% |
4 | -0.52% |
5 | -0.67% |
6 | -0.45% |
7 | -0.30% |
8 | -0.01% |
9 | +0.15% |
10 | +0.51% |
A | +0.59% |
These percentages are based on a single deck. If you’re
playing in a game with multiple decks, the effect of the removal
of each card is diluted by the number of decks in play.
playing in a game with multiple decks, the effect of the removal
of each card is diluted by the number of decks in play.
Looking at these numbers is telling, especially when you
compare these percentages with the values given to the cards
when counting. The low cards (2-6) have the most dramatic effect
on the house edge. That’s why almost all counting systems assign
a value to each of them. The middle cards (7-9) have a much
smaller effect. Then the high cards, aces and tens, also have a
large effect.
compare these percentages with the values given to the cards
when counting. The low cards (2-6) have the most dramatic effect
on the house edge. That’s why almost all counting systems assign
a value to each of them. The middle cards (7-9) have a much
smaller effect. Then the high cards, aces and tens, also have a
large effect.
The most important cards are the aces and the fives. Each of
those cards is worth over 0.5% to the house edge. That’s why the
simplest card counting system, the ace-five count, only tracks
those two ranks. They’re that powerful.
those cards is worth over 0.5% to the house edge. That’s why the
simplest card counting system, the ace-five count, only tracks
those two ranks. They’re that powerful.
You can also look at the probability that a dealer will bust
based on her up card. This provides some insight into how basic
strategy decisions work.
based on her up card. This provides some insight into how basic
strategy decisions work.
Dealer’s Up Card | Percentage Chance Dealer Will Bust |
---|---|
2 | 35.30% |
3 | 37.56% |
4 | 40.28% |
5 | 42.89% |
6 | 42.08% |
7 | 25.99% |
8 | 23.86% |
9 | 23.34% |
10 | 21.43% |
A | 11.65% |
Perceptive readers will notice a big jump in the probability
of a dealer busting between the numbers six and seven. They’ll
also notice a similar division on most basic strategy charts.
Players generally stand more often when the dealer has a six or
lower showing. That’s because the dealer has a significantly
greater chance of going bust.
of a dealer busting between the numbers six and seven. They’ll
also notice a similar division on most basic strategy charts.
Players generally stand more often when the dealer has a six or
lower showing. That’s because the dealer has a significantly
greater chance of going bust.
Summary and Further Reading
Odds and probability in blackjack is a subject with endless
ramifications. The most important concepts to understand are how
to calculate probability, how to understand expected value, and
how to quantify the house edge. Understanding the underlying
probabilities in the game makes learning basic strategy and card
counting techniques easier.
ramifications. The most important concepts to understand are how
to calculate probability, how to understand expected value, and
how to quantify the house edge. Understanding the underlying
probabilities in the game makes learning basic strategy and card
counting techniques easier.